I suggest you ...

Add Pokemon moves

It's would be nice if you had the moves Pokemon learn as they level up. Plus the tutorial and hm and tm skill there compatible with learning too. So far it's good but would be awesome with that information being added

I agree that it is a very useful and important information to know HOW a Pokémon learns WHICH moves.

Actually you can already find out the ‘WHICH’ by going to the simulator, choosing the Pokémon you like and tapping on a move slot which will only bring up a list of moves that your chosen Pokémon can learn.

But of course there are two disadvantages about this:
1. this is far more complicated than it could be
2. there’s no info about HOW to learn the moves yet

Thus the requested functionality isn’t there yet and as I agree on its necessity expect it to be there in a future update, hopefully already in version 1.1 which is scheduled for mid august.